Let Sn(x)= nx/(nx+1)
Compute the pointwise limit of Sn on [0,1].
Is the convergence uniform?
all we did was to take the limit as
Is it uniform? there are several ways to attack this.
what do we know about the limit of a uniformly continuous function?
we could also use the definition for uniform convergence
we could also check to see whether or not in which case it is uniformly convergent if it is 0